I've got a significant interaction effect and I'm unsure how to interpret and report the results.
In my experiment, I've got plants planted inside fences to protect them from deer (fence plots) and outside fences where they can be eaten (open plots). Within each plot, half the area of gm (garlic mustard) was removed. Before any gm was removed, the initial % cover of gm (ipc.gm) was measured in each subplot.
height4 = final plant height
height = initial plant height
ipc.gm = initial % cover of gm
fence = factor with 2 levels: Fence, Open
gm = factor with 2 levels: removed, gm
plot/subplot = random effect variable
model <- lme(height4 ~ height + ipc.gm * fence * gm, random = ~1|plot/subplot)
> anova.lme(model, type = "marginal") numDF denDF F-value p-value (Intercept) 1 92 0.821069 0.3672 height 1 92 30.827557 <.0001 ipc.gm 1 92 0.673770 0.4139 fence 1 8 15.483526 0.0043 gm 1 8 1.066909 0.3319 ipc.gm:fence 1 92 5.021460 0.0274 ipc.gm:gm 1 92 0.023078 0.8796 fence:gm 1 8 1.967297 0.1983 ipc.gm:fence:gm 1 92 2.088226 0.1518
The main effect of fence is significant (P = 0.0043).
> emmeans(model, ~ fence) NOTE: Results may be misleading due to involvement in interactions fence emmean SE df lower.CL upper.CL Fence 24.00245 1.052951 3 20.651490 27.35341 Open 11.67182 1.347438 3 7.383666 15.95996 Results are averaged over the levels of: gm Degrees-of-freedom method: containment Confidence level used: 0.95
Plants were taller in Fenced plots (24 cm) than in Open plots (11.7 cm).
The main effect of ipc.gm is not significant (P = 0.4139), but the interaction term ipc.gm:fence is significant (P = 0.0274).
This means that the effect of ipc.gm depended on the level of fence
Plotting height4 ~ ipc.gm, subset by fence level (package: lattice):
xyplot(height4 ~ ipc.gm, group = fence, type = c("p","r"), auto.key = TRUE)
It appears that height4 increases with increasing ipc.gm, but only in fence plots.
My questions are:
- How do back up my statement "height4 increases with ipc.gm but only in fence plots" with stats? Do I just need to report the slopes of the lines? Or do I need to do a statistical test that show the slope of the line is significantly different from zero?
- How do I get the slope coefficients of height4 ~ ipc.gm, subset by fence level?
- What statistical test (if any) do I need to use to show that height4 increases with ipc.gm in Fence plots, and that height4 is unaffected by ipc.gm in Open plots